Metadata is data/information about data.
The tags in the provides metadata about the HTML document. Metadata are machine readable, and won't be displayed on the page. Metadata usually specifies the page description; author; the date of publication or the date of the last update; keywords, etc. Thankfully it's supported by all the common browsers including Google Chrome, Internet Explorer, Mozilla, Opera, and Safari.
Meta keywords aren't used as a ranking factor in search engine algorithms, so these can probably be ignored. However, meta titles and meta descriptions are still important for any web page.
A meta description is a short HTML attribute found in the header of the webpage. It's usually 150 characters - including spaces - and displays under the title tag and link in search results. Search engines have limited space and aren’t capable of displaying long meta descriptions.
When you fail to provide a meta description, search engines will generate a description from the website page content. With WordPress you can choose to install plugins such as Yoast to help with this.
Sometimes search engines may overrule the meta description a developer has specified in the HTML of a page. Helpful content will be chosen from the main body of the page. This stops people writing unrelated content in the website meta description.
Meta descriptions aren't a ranking factor, however a good description will likely increase the number of clicks to your website from search engines. For that reason, it's important to put effort into the meta descriptions.
It's good practice to avoid duplicate meta description tags. For large websites, such as eBay, an algorithm can be used to pragmatically produce the tags.
Once meta descriptions have been carefully written, it's worth thinking about Facebook Open Graph. These tags control how your website pages appear on social media pages. You can also look into Twitter cards.
It's worth signing up for Google Webmaster Tools, for free, to diagnose any potential issues with metadata. They'll inform you if you have any duplicate tags.